This paper marks 20 years of developments within the area of the Multiplicative Error Models, starting from the seminal paper of [1]}. Overall, the conceptual advantages of using a \(\mathsf {MEM}\)  lie in the fact that positive processes can be modeled directly without a log–transformation, and that GMM inference is widely available avoiding the need for a parametric specification of the error distribution. Residual diagnostics typically improves relative to non–multiplicative specifications, especially in what concerns autocorrelation. In forecasting, the various versions of the \(\mathsf {MEM}\)  have proved successful, especially in reproducing the dynamic behavior of realized volatility [2]}, but also of intradaily volumes [3]} for Volume Weighted Average Price (VWAP) applications [4]}.
